Judy, I'm not sure you need to panic. In our climate vinca can be an aggressive groundcover in the right conditions but not what I'd consider to be an invasive one, certainly not like a few others I could mention. First, unless it has the perfect conditions (part shade, rich soils, even moisture) it is not quick to establish. Even when established, it is relatively easy to keep in check by cutting back or pulling up plants that creep where they are not wanted. I have had vinca minor (planted intentionally by me) in my backyard woodland garden for years. It has not spread outrageously but nicely carpets an area under trees and larger shrubs and even accomodates a colony of windflowers. It has not smothered anything, including a few perennials in the area, and even the odd weed pokes through.

If you are really concerned about its encroachment, perhaps you could establish a no-vinca zone along the two yards by creating what would be almost a small dry stream bed of river rocks. Doesn't have to be especialy wide, would be more natural looking than any type of artificial barrier and relatively easy to maintain. Since vinca spreads by rooting along its stems, just pull up the plants that venture outside the bounds. It is far easier to deal with than aggressive groundcovers that spread by rhizomes or underground stolons like ivy, hypericum, gallium or lamiastrum.

Gardengal -

Thanks for your knowledgeable reply! I think I will use that dry stream bed idea. I'm going to put landscape fabric underneath the rocks and that will also help keep out weeds.

Just curious if bricks sunk on their sides into the dirt between the two properties would also work, say with about four inches of the brick underground and four inches above ground. If I went that route I would plant dwarf boxwoods next to the brick just so that it would look more decorative.

Does the vinca also spread by seeding itself around?

The bricks will work fine as long as they're placed tightly against each other. Vinca does not self seed.